CHAPTER 1: INTRODUCTION

Transcription

1 1 CHAPTER 1: INTRODUCTION Increasing environmental concerns and escalating conventional energy supply costs are creating a resurgence of interest in solar energy (CANMET, 1993). The changing infrastructure of utilities in the United States has provided an opportunity for new initiatives in Solar Domestic Hot Water (SDHW) Systems. In particular, the opportunity exists for utilities to market SDHW systems to customers with both customer and utility cost savings. A significant area of interest is the development of low-flow solar domestic hot water systems. Previous work indicates that the total flow volume through the collector for an average day should be matched to the volume supplied to the load by solar for an average day for direct SDHW systems (IEA, 1996). Low-flow systems are capable of reducing equipment and installation costs which together account for approximately two-thirds of the total SDHW system cost. Low-flow systems allow equipment to be considerably sized down; piping and pumps are smaller. Cost advantages are in terms of decreased material costs, less parasitic pumping power required from the utility and reduced costs with installing lightweight systems. The thermodynamic advantage of low-flow systems is increased tank stratification, which leads to improved system performance.

2 2 In many climates, freeze protection is required in the form of a glycol-water heat exchanger. Low-flow systems influence the heat exchanger performance. The flow rates required on either side of the heat exchanger need to be determined in order to optimize system performance. Low-flow solar domestic hot water systems also offer a new area of investigation: PV pumping. The lower pumping power now required by low-flow systems can be met with a PV pump. The PV driven pump offers many advantages in terms of better control strategies and no need for an auxiliary power source. 1.1 Water Heating Costs Residential water heating accounts for approximately 18 % of the annual energy consumption in the residential sector of the United States (DOE, 1997). The residential sector energy use is shown in Figure 1.1. Space Heating 53% Appliances 24% Water Heating 18% A/C 5% Figure 1.1 Residential sector energy use

3 Most utilities are summer peaking, meaning that the highest demand is due to cooling loads on 3 the hottest sunniest days. Water needs are generally insensitive to climatic changes rendering solar domestic hot water heating in a good position to alleviate utility energy demands. Currently, low natural gas prices result in natural gas being the fuel of choice to meet the future demand for electricity. It will be difficult for solar energy to be competitive in areas where natural gas is available. However, there are many regions where natural gas is not accessible. Solar water heating can be a viable and competitive alternative. The costs of operating and installing different types of water heaters over a life cycle of thirteen years (the average lifetime of a water heater) is presented in Table 1.1. These data are based on the following 1995 fuel costs: $0.52/therm for gas and $0.07kWh for electricity.

4 4 Fuel Type estimated purchase price installed estimated yearly operating costs estimated life cycle cost, 13 years of operation Gas highefficiency* $470 $128 $2, gallon gas $435 $144 $2,307 low efficiency* Gas side vent* $850 $134 $2,592 Electric heat $2000 $123 $3,599 pump* Electric highefficiency* $580 $331 $4, gallon $475 $349 $5,012 electric low efficiency* Solar system # $2560 $10 $2,690 *Madison Gas and Electric, 1995 #International Energy Agency, Table 1.1 Water Heater Life Cycle Costs The other costs of gas and electricity are often overlooked. Gas and electricity are the culprits producing air pollutants including sulfur dioxide, nitrogen oxides, particulates and heavy metals which impact human health, flora and fauna, building materials, and social assets like recreation and visibility. Greenhouse gases including carbon dioxide, methane, and chlorofluorocarbons are suspected of contributing to global climate change and pose potential impacts on agriculture and human health. Water use and water quality are affected by electricity production, principally through thermal pollution or hydroelectric projects that affect aquatic populations. Land use is also affected by power plant sites and by waste disposal including solid, liquid and nuclear wastes (DOE, 1995).

5 1.2 SDHW Barriers 5 There are a number of barriers that have prevented the widespread adoption of solar water heaters by both utilities and homeowners in the past. These have included high capital costs, a reputation for poor system reliability, an inadequate system infrastructure and limited public knowledge of the gains and benefits of current technology (CANMET, 1993). With deregulation and new competition, utilities are seeking innovative new products and services that will add value and produce customer loyalty. Utilities can experience demand reduction from solar water heating systems during peak times, typically morning and evenings when hot water draws tend to be the greatest. The energy reduction eliminates the need for larger power plant generating capacities and pollution from power plants is reduced as loads decrease. Many electricity-providing utilities are losing customers who are switching to cheaper gas; solar hot water heating may provide a means of retaining customers. Many utilities are now employing Energy Service Companies (ESCOs). The concept presents the possibility of converting solar water heating from a subsidized Demand Side Management program to a profitable business. The ESCO is typically responsible for the installation, service and maintenance of the solar hot water system. In return for contributing to an increased market size, the ESCO receives a portion of performance savings from the utility. The Utility on the other hand receives a monthly service fee from the homeowner in return for the services the ESCO provides. The homeowner experiences no first costs and is assured reliability and maintenance of the system. The ESCO concept is demonstrated in Figure 1.2 (Enstar, 1996).

6 6 Figure 1.2 Schematic of the ESCO concept This end-use pricing, which involves the sale of solar heated water itself, rather than the sale or lease of equipment that makes it, is believed to increase market penetration. The increased demand will have a positive effect on the economics of solar water heating (Lyons and Comer, 1997). 1.3 Solar Domestic Hot Water Systems The primary components in a solar domestic hot water system are a solar collector, a tank, a pump and a controller. The function of the solar collector is to absorb solar radiation by means of an absorber surface, which is usually a black copper plate, and convert it into thermal energy. The thermal energy is then conducted to a flowing fluid by means of copper tubes welded to the absorber surface. The collector is protected from convective losses with a glass cover that is

7 transparent to incoming long-wave radiation, but prohibits short wave radiation leaving the 7 collector. Insulating material is usually placed along the sides and back of the collector. The tank is the storage media for the heated water. It is common to use retrofitted conventional gas water-heater tanks. A pump is normally controlled by a differential temperature-sensing controller that turns on the pump when the collector outlet temperature is greater than the temperature in the bottom of the tank. Auxiliary heat is usually added by means of a heating element inside the tank or as an external zip heater. The components above form a direct solar domestic hot water system such as the one shown in Figure 1.3. Figure 1.3 Direct solar domestic hot water system (not to scale) Some form of freeze protection is required in many climates. One method of freeze protection is to use a heat exchanger where antifreeze is circulated in the collector-side loop and water in

8 8 the tank-side loop. An example of such an indirect solar domestic hot water system is shown in Figure 1.4. Figure 1.4 Indirect solar domestic hot water system (not to scale) A means to easily assess the performance of a system is to determine the solar fraction, given by equation 1.1. Qauxiliary SF = 1 (1.1) Q load where Q auxiliary is the auxiliary heat requirement needed to meet the load, given by Q load. The solar fraction is the proportion of the load that is met by solar energy. The difference between the load energy requirement and the auxiliary energy input is the amount of solar energy gained. Flow rates through solar systems are usually given per unit area of the collector with units of kg/s.m 2.

9 1.4 Simulating Systems 9 Simulations provide a means of predicting and optimizing a system. System performance is best analyzed with a simulation package, such as TRNSYS, whilst individual system components can be readily analyzed with analytical solutions, equations and numerical methods. TRNSYS is a transient system simulation program with a modular structure. The system description is specified in a deck in which the user can specify the system components and how they are connected. The program comes equipped with a library of components commonly found in thermal energy systems, as well as component routines to handle input of weather data and output of simulation results. The advantage of using such a program is that its modularity facilitates the addition of mathematical models, referred to as TYPES. One can easily observe the variation of certain parameters on a system, which would be costly to analyze experimentally. Meteorological information including horizontal surface radiation, tilted surface radiation, wind speed, and ambient temperature are used as inputs describing the environmental conditions specific to each location. Each component, specified by a TYPE, has its own parameters and input and output variables. The components are readily linked together by combing the output variables of one component to the input variables of another component.

10 Load Profile Hot water usage profiles used in this research were adapted from WATSIM software by Williams (1996). The 8760 hourly water draw profiles were based on the standard water draw specification file provided in the WATSIM program. The neutral household of four draw profile has been chosen. The neutral household of four s water draw lies between water draws of conservative and profligate households. The average daily hot water draw is about 77.2 gallons per day (12.2 kg/hr). 1.6 Thesis Objective Residential hot water use represents a large proportion of residential energy use. The residential energy use accounts for approximately one third of the total energy use. Utilities can use enduse pricing to target solar domestic hot water heating. This offers many benefits in terms of increased market share and reduced demand at the generation level in an increasingly competitive environment. The development of low-flow solar domestic hot water systems does not only provide a cost-effective alternative in hot water systems, but can also reduce emissions and demand at the generation level. This thesis demonstrates some strategies in designing an optimal low-flow system.

11 11 CHAPTER 2: LOW-FLOW SOLAR DOMESTIC HOT WATER SYSTEMS The conventional strategy in designing solar domestic hot water systems has been to maximize the solar collector heat removal factor (and the heat exchanger energy transfer coefficient for indirect systems) while attempting to minimize parasitic power. The Hottel-Whillier equation (Duffie and Beckman, 1991) given in equation 2.1 defines the efficiency for a solar collector in terms of the collector heat removal factor F R, given in equation 2.2. η i = F R [ G ( τα ) U ( T T )] T av G T L i a (2.1) F R mc & A cu LF' 1 exp (2.2) mc & p = AcU L p where G T = the solar radiation (W/m 2 ) (τα) av = the average transmission-absorption product given by the cover and absorber configuration U L = the collector loss coefficient (W/m 2 K) T I T a = the temperature of the collector inlet fluid (K) = the ambient temperature (K).

12 12 In Equation 2.2, m& = the collector fluid flow rate (kg/s) C p = the collector fluid specific heat (J/kg.K) A c = the collector area (m 2 ) F = the collector efficiency factor More details on the collector heat removal factor will be given in chapter 3. Observing equation 2.1, it can be seen that increasing the mass flow rate will indeed increase the collector heat removal factor, but this does not necessarily mean the collector efficiency given by equation 2.2 will increase. As the collector flow rate is increased the collector inlet temperature may be higher due to tank mixing and therefore the losses will be higher (Van Koppen et al. 1979). An alternative to maximizing the collector heat removal factor is to increase tank stratification. Increased stratification causes the temperature gradient along the height of the tank to be larger meaning the temperature at the top of the tank is much greater than the temperature at the bottom of the tank. In the past, the average flow rates have been high and resulted in an average daily collector flow rate that is three or more times greater than the average daily hot water draw (Fanney and Klein, 1988). The tank is usually sized to the average daily load, thus storage fluid is recirculated through the collector loop three or more times a day.

13 13 Naturally, the tank will stratify when there is no circulation. When there is solar energy collection, there will be circulation and the tank will become mixed. It has been confirmed experimentally that at lower flow rates higher stratification exists (Fanney and Klein, 1988). The optimum flow rate is found to be approximately 10 to 33% of that typically used in forced circulation direct systems (Fanney and Klein, 1988). Wuestling, Klein and Duffie (1985) found the optimum performance for a system without a heat exchanger is achieved when the monthly average daily total water circulated through the collector array is approximately equal to the average daily total load. Fanney and Klein (1988) performed side by side tests on identical SDHW systems. One system had a kg/s.m 2 collector array flow rate, which was in accordance with manufacturer s recommendations. The other system was based on observations of tank stratification given by Van Koppen et al (1979) and Wuestling (1983) with a kg/s.m 2 collector array flow rate. The system with the lower collector flow rate resulted in an 8% increase in solar energy delivered to the storage tank and a 10% decrease in auxiliary energy consumption. 2.1 Simulating Tank Stratification Stratified tank models fall into two main categories, the multi-node approach and the plug flow approach. The multi-node approach involves dividing the tank into N sections or nodes and performing an energy balance for each node. The plug flow approach assumes that segments of

14 14 liquid at various temperatures move through the tank in plug flow; the model keeps track of the size, temperature and position of the segments. TRNSYS Type 60 simulates a stratified fluid storage tank using the multi-node approach. The tank is assumed to contain equal volume segments or nodes (however, there is an option to use unequal size nodes). Using one node simulates a fully mixed tank. Increasing the number of nodes decreases internal mixing and a higher degree of thermal stratification is achieved. It is important to determine the sensitivity of the number of nodes chosen. Up to 100 nodes may be chosen, but increasing the number of nodes substantially increases the computing time. It is necessary to find the minimum number of nodes to reasonably model the effects of stratification. Figures 2.1 and 2.2 show the effects of the solar fraction for the number of nodes for two locations, Madison, Wisconsin and Miami, Florida. The flow rate is given per collector area, rendering the plots independent of collector area.

15 Solar Fraction nodes 20 nodes 10 nodes 3 nodes node flow rate [kg/s.m 2 ] Figure 2.1 Sensitivity to the number of nodes for Madison, Wisconsin nodes 20 nodes 10 nodes Solar Fraction nodes 1 node flow rate [kg/s.m 2 ] Figure 2.2 Sensitivity to the number of nodes for Miami, Florida.

16 16 Increasing the nodes and hence the degree of stratification increases the solar fraction. At low collector flow, the simulation results obtained for maximum stratification agree well with the experimental results (Fanney and Klein, 1988). It can be seen that the difference between 20 and 50 nodes is very small. Since 50 nodes require too much computing time, 20 nodes will be used in this research for all simulations. The optimum collector flow can be shown independent of location and the time of the year by comparing Figure 2.1 and Figure 2.2. The average daily load draw is kg/s.m 2. The average daily load was found by averaging the hourly loads of the load profile over the year for the hours of sunshine, approximately 8 hours each day. This value is close to the optimum flow rate for both locations. Another important factor is the tank storage size. An undersized tank will force recirculation, whereas an increased tank size will incur additional material costs and increase convection losses to the environment through the increased surface area. Figure 2.3 demonstrates the effect of the variation of tank volume on solar fraction. The tank losses have been assumed negligible; if they were included, increasing the volume would increase the losses to the environment and therefore the solar fraction would decrease.

17 average daily load = m Miami, Florida 0.80 Solar Fraction Madison, Wisconsin Tank Volume/Average Daily Load Figure 2.3 Effects of variation of tank volume for two locations, Madison, Wisconsin and Miami, Florida. Figure 2.3 demonstrates the optimal tank volume is independent of location. A tank volume of about 0.4 m 3 is the optimal for the given load. Decreasing the storage volume will not allow the tank to fully stratify. Further increasing the tank volume will have little effect on the solar fraction until a volume is reached were convective losses to the environment are so large that the solar fraction is reduced. A tank volume of 0.4 m 3 will be used for all simulations in this research. 2.2 Conclusions Reducing the flow rate can significantly improve solar gains as tank stratification is improved. However, the storage tank volume, daily load, and load distribution have a direct effect on the

18 18 optimum fixed flow rate because they directly contribute to the amount of tank recirculation. Careful selection of tank size and number of nodes need to be considered. For the given load profile 20 nodes model maximum tank stratification without drastically increasing the computing time. A tank volume of about 0.4 m 3 is about the optimal size in terms of material savings and maximum stratification.

19 19 CHAPTER 3: COLLECTOR PERFORMANCE Solar collectors function as heat exchangers; they receive solar radiant energy and transfer it to the flowing fluid. The useful energy gain of the collector determines the temperature rise of the flowing fluid in terms of design and operational variables. Equation 3.1 (Duffie and Beckman, 1991) expresses the useful energy gain of a solar collector in the following form. Q u c R [ G U ( T T )] = A F (τα) (3.1) T L i a where F R is the collector heat removal factor, (τα) is the transmittance absorptance product, U L (W/m 2.K) is the overall loss coefficient, A c (m 2 ) is the collector area, G T (W/m 2 ) is the incident radiation and T i (K) and T a (K) are the fluid inlet and ambient temperatures respectively. The collector heat removal factor, F R, is the ratio of actual useful energy gain of a collector to the useful gain if the whole collector surface were at the fluid inlet temperature, equation 3.2.

20 20 F R = A c mc & p ( To Ti ) [ G ( τα ) U ( T T )] T L i a (3.2) In equation 3.2, m& is the mass flow rate, C p (J/kg.K) is the specific heat of the collector fluid and T o (K) is the fluid outlet temperature. F R is analogous to the heat exchanger effectiveness. Radiation passes through the cover system and is incident on the absorber plate. Some radiation is reflected back to the cover system, which again may be partly absorbed and reflected by the plate. The transmittance-absorptance, (τα), represents the overall effect of a cover-absorber combination rather than the product of the two properties. Energy is transferred to the surroundings from the top, sides and bottom of the collector. This energy transfer rate is given in terms of the overall loss coefficient, U L (W/m 2.K). A relation for U L (Duffie and Beckman, 1991) is given in equation 3.3. U = U + U + U (3.3) L top edge back where an approximate relation for U top (W/m 2.K) given by Klein (1975) is shown in equation 3.4, and U edge (W/m 2.K) and U back (W/m 2.K) are the losses from the edge and back of the collector respectively. U top = C T pm ( T T ) N pm G 1 N + G f a h w + ε p σ N 2 2 ( T + T )( T + T ) G pm G G ( 1 ε ) ε p a pm 2N + g a + f 1 N (3.4)

21 21 where N G = number of glass covers 2 f = ( h h )( N ) w 2 C = ( β β ) w G β ε g ε p T a T pm =collector tilt (degrees) = emittance of glass = emittance of plate = ambient temperature (K) = mean plate temperature (K) T pm Q c = Ti + 1 FRU L u A ( F ) R h w = wind heat transfer coefficient (W/m 2.C) It can readily be determined from equation 3.2 that the heat removal factor is heavily dependent on flow rate at low flow rate values. At high flow rates, F R becomes independent of flow rate. Reducing the collector flow rate is detrimental to the collector heat removal factor. It is pertinent to find the configuration and geometry that is most appropriate in terms of pumping power and collector efficiency (defined in equation 2.1). In this analysis the popular headerriser flat-plate collector and the serpentine flat-plate collector will be analyzed and compared.

22 Header/Riser Flat-plate Collector The header-riser flat-plate collector consists of two horizontal headers and a series of parallel, vertical risers as shown in Figure 3.1. Figure 3.1 Conventional flat-plate collector The analysis of the header-riser flat-plate collector makes many assumptions (Duffie and Beckman, 1991). These include the following: Headers can be neglected since they cover a small area. The headers provide uniform flow to tubes. Heat flow through the cover is one-dimensional. Temperature gradients around the tubes can be neglected. The temperature gradients in the direction of flow and between the tubes can be treated independently.

23 23 One primary concern is how these assumptions hold for low flow. It will be shown that the flatplate collector does not have equal flow rates through the risers. The pressure drops from the bottom to the top of the risers are greater at the ends than the center of the collector. This leads to higher flows in the end risers and lower flows in the center risers Pressure Distribution Fanney and Klein (1985) experimentally found that for low flow rates (less than kg/sm 2 compared to the manufacturer s recommended flow rate of kg/sm 2 ) there was an imbalance in the flow through a collector array. The flow was not divided equally between three individual collectors. The imbalanced flow condition was detected by monitoring thermocouples attached to the absorber plates. However, the individual collectors were not examined for flow imbalances. Dunkle and Davey (1970) state that the efficiency of large solar water heating installations is reduced if flow is not uniformly distributed through the absorber. They found that flow is short circuited through the first and last few risers leaving a dead zone of low flow near the center of the bank. In these regions of low flow rates, there are higher heat losses and lower thermal efficiency due to the higher temperatures in these areas. Temperature distribution is the worst at the highest flow rate. Dunkle and Davey also state that free convection forces counterbalance the short circuit effect when the absorbers are inclined.

24 24 A model of the pressure distribution was developed by using mass balances and momentum balances at each node. A node is defined at each bend or pipe intersection of the collector. For each node, the mass flowing in and out was determined and the pressure was found from the head loss and the preceding node pressure. Figure 3.2 represents a simplified collector with two risers. Figure 3.2 Simplified collector with two risers For the above Figure, the momentum balance is represented in equations 3.5.

25 , i, i, i, i, i, i D Lv f P P D Lv f P P D Lv f P P D Lv f P P D Lv f P P D Lv f P P + = + = + = + = + = + = r r r r r r ρ ρ ρ ρ ρ ρ (3.5) In equations 3.5, ρ (kg/m 3 ) is density, f is the friction factor evaluated from the Moody Chart, L (m) is the length of each header or riser segment, v r (m/s) is the velocity, which is found from the mass flow rate, and D i (m) is the inner diameter of the tube. The mass balance is given in equations 3.6, where m& (kg/s) is the mass flow rate through each segment ,,,,,,,,,, m m m m m m m m m m & & & & & & & & & & = = + = + = (3.6) Gerhart and Gross (1985) give loss coefficients for Tee joints that were used at the header and riser joints. The collector is arranged in such a way that the headers form the line flow of the tee joint and the risers form the branch flow. The loss coefficients for the branch and line flow used

26 26 were estimated from the data given by Gerhart and Gross. Loss coefficients are used to find an equivalent length that is added to length of the header or riser when calculating the pressure loss. The equivalent length is found using equation 3.7, where K is the loss coefficient, D (m) is the pipe diameter and f is the friction factor. KD L equivalent = (3.7) f The technical data for the Alta Energy Liquid Flat-plate Collector Model ATL recommends flow rates of 0.75 gpm to 1.5 gpm that result in pressure drops of 0.01 to 0.04 psi. The Alta Energy collector has a net area of 22.1 ft 2. The risers comprise of 3/8-inch copper tubes spaced 2 inches apart from the centers and the headers are one inch in diameter. The pressure drops calculated for the Alta Energy collector geometry agree with the specified pressure drops given by the manufacturer as shown in Figure Pressure Drop [psi] manufacturer's data m [gpm] Figure 3.3 Flow rates and corresponding pressure drops

27 27 Flow through the flat-plate collector becomes more evenly distributed as the flow rate is reduced. Figure 3.4 shows the dimensionless flow rate through the collector, that is, the flow rate through the riser divided by the flow rate entering the collector as a function of riser number. As the mass flow rates increase, the relative flow through the outer risers increases while the relative flow rates in the inner risers decreases m riser /m in kg/s.m kg/s.m kg/s.m kg/s.m Riser Figure 3.4 Flow distribution through a collector with varying flow rates The imbalance found by Fanney and Klein is at odds with the above analysis which indicates that flow imbalance should decrease with decreasing flow rate. The reason that Fanney and Klein s results differ may be because they were measuring temperature and not flow.

28 28 In order to verify, that the discrepancy was not based on the loss coefficients at the joints, the collector was modeled with varying loss coefficients. The loss coefficients were randomly chosen. The coefficients for the headers vary from 1.45 to 2.7. The loss coefficients for the risers vary from 0.8 to 1.5. It was still found that the low-flow model had the most evenly distributed flow m riser /m in kg/s.m kg/s.m kg/s.m kg/s.m Riser Figure 3.5 Flow distribution for varying the loss coefficients The pressure drop along the headers for the common situation of water entering the bottom header on one side of the collector and leaving the top header on the other side was also determined. Figure 3.6 demonstrates the dimensionless pressure through the headers.

29 Lower Headers kg/s.m kg/s.m kg/s.m 2 P header /P drop Upper Headers 0.02 kg/s.m kg/s.m kg/s.m kg/s.m kg/s.m Riser Figure 3.6 Pressure distribution through a collector with varying flow rates Again, these results are in agreement with Dunkle and for flow distribution through arrays of flatplate collectors. Lowering the flow rate has the positive effects of a more even flow distribution and pressure drop across the bank of risers Collector Heat Removal Factor For a header-riser flat-plate collector, the collector heat removal factor can be expressed as shown in equation 3.8 (Duffie and Beckman, 1991). F R mc & A cu LF' 1 exp (3.8) mc & = p AcU L p

30 30 where F is the collector efficiency factor shown in equation 3.9. F' = W U L 1 1 U L 1 [ D + (W D )F ] C b πdi hfi (3.9) In equation 3.9, W (m) represents tube spacing, C b (W/m.K) is the contact resistance, h fi (W/m 2.K) is the internal fluid heat transfer coefficient and F is the standard fin efficiency, given in equation F [ m( W D) / 2] ( D) / 2 tanh = (3.10) m W Further details of the standard fin efficiency and the internal fluid heat transfer coefficient will be given in section 3.4. It can be seen from this equation that increasing the flow rate will indeed increase the heat removal factor. In the past, this has led to the conclusion that higher flow systems will yield better results. However, low flow rates have the advantage of allowing the storage tank to stratify. This means that the temperature gradient along the height of the tank will be high. Hotter fluid will be available to meet the load and colder fluid will circulate through the collector loop. The temperature rise across the collector will be higher due to the lower flow rates. An added advantage is the decreased cost associated with pumping the fluid. Since low-flow

31 31 systems may give an overall better system performance, the best collector design must be determined. The serpentine collector design is a viable alternative, as the flow rates are low, the higher-pressure drops through the serpentine collector are of little concern. It has already been shown that for low flow the header-riser flat-plate collector will have an even flow distribution, but the lower flows through each riser may adversely affect the heat transfer coefficients and hence performance. 3.2 Serpentine Flat-plate Collector Serpentine collectors consist of a flow duct that is bonded to the absorber plate in a serpentine or zigzag fashion. A serpentine collector is shown in Figure 3.7. Figure 3.7 Serpentine flat-plate collector Pressure Distribution The pressure drop for a serpentine collector is easily calculated from equation total = (3.11) P ρf L 2D r v i

32 32 In equation 3.11, L total (m) is the tube length plus the equivalent length for the losses at the bends. Clearly, the pressure drop increases with increasing flow rate and with total length Collector Heat Removal Factor The heat removal factor for a serpentine collector is much more difficult to determine than for a conventional flat-plate collector. Unlike the analysis for the header-riser flat-plate where the fins between the tubes are assumed adiabatic at the center of the tube spacing, there is heat transfer between the tubes for a serpentine collector. Abdel-Khalik (1976) analyzed the heat removal for a flat-plate solar collector with a serpentine tube. This analysis produced graphical results to obtain the heat removal factor. Figure 3.8 represents the generalized chart for estimating the heat removal factor, F R, for flat-plate collectors with serpentines of arbitrary geometry and number of bends. The parameters F 1 and F 2, given in equations 3.12 and 3.13 respectively, are functions of physical design parameters, including plate thickness, conductivity and tube spacing.

33 33 F R /F F 2 = mc p /F 1 U L A c Figure 3.8 Generalized chart for estimating the heat removal factor by Abdel-Khalik F 1 2 NκL κr(1 + γ ) 1 γ κr = (3.12) U A L c 2 2 [ κr(1 + γ ) 1] ( κr) 1 F2 = (3.13) 2 κr(1 + γ ) 1 γ κr where kδm κ = (3.14) ( W D) sinh m γ DU = 2 cosh m L (3.15) κ U L m = ( W D) (3.16) kδ

34 34 In the above equations, D (m) is the outer tube diameter, k (W/m.K) represents the plate conductivity, δ(m) is the plate thickness, R (m.k/w) is the resistance between the tube and the plate and N is the number of turns in the serpentine collector minus one. R is a thermal resistance defined by equation R = + C πd h b i fi (3.17) Abdel-Khalik states that the differences in the values of F R /F 1 for one turn, (N=2) and those obtained numerically for higher values of N are less than 5 %. These differences vanish completely for & F U A greater than unity. In other words, the graphical results are valid mc p / 1 L c within 5% for all practical situations. Zhang and Lavan (1985) argue that this is not the case. Zhang and Lavan present an analytical solution to Abdel-Khalik s analysis for N=2 or for the case where the parameter, & F U A is greater than unity. They also provide analytical solutions for N=3 and N=4, mc p / 1 L c however these are in matrix form and difficult to implement. Zhang and Lavan state that the heat removal factor, F R, is generally a maximum at N=1 and is generally a minimum at N=2. As N increases, F R increases, but at a decreasing rate. For N, F R seems to approach the value for F R at N=1. As the number of turns increases, the tube length increases for a given area. The surface area exposed to solar radiation increases

35 and F R increases. When N=1 the serpentine collector acts as a header-riser flat-plate and F R is the largest since there is no heat transfer between tubes. 35 Lund (1989) also finds the heat removal factor independently of the methods above. In his analysis, he expresses serpentine performance in terms of an effectiveness-ntu relationship. Lund couples conduction and transport equations that are rendered in non-dimensional form using a shape factor. The shape factor is determined by duct shape and conduction through the duct from the absorber plate. Lund s analysis seems to be most useful for turbulent flow because heat transfer is increased for turbulent flow. In this flow regime, for N=2 the results are consistent with those obtained by Zhang and Lavan. Chiou and Perera (1986) also analyzed the serpentine collector for any number of turns. The results are presented in awkward matrix forms. They show that the thermal efficiency of the solar collector for a serpentine tube arrangement is less than that for a header-riser configuration for most of the day. During the morning hours and late afternoon, the serpentine collector performs better in terms of the heat removal factor. The flow rate used is kg/s. Chiou and Perera conclude there are two possible reasons for this. First, there is a higher-pressure drop associated with the serpentine collector that may create flow imbalances; therefore, the flow imbalances will cause poor heat transfer. Second, the heat transfer between the fluid and the plate reduces toward the outlet of the serpentine collector. The difference is most likely due to an overall lower collector-plate temperature for the header-riser flat-plate collector and therefore decreased thermal losses.

36 36 For practical applications, serpentine collectors have many turns, and therefore it is necessary to calculate F R with a simple method. The matrix solutions are cumbersome to implement. 3.3 Finite difference technique A finite difference technique was developed. Abdel-Khalik presents analytical equations for heat flow per unit length entering the base of the tube, given in equations In these equations, m is given by equation 3.15 and T bi (K) is the temperature at the base of the plate for the segment i. q q q + i = κ [ θi 1 θ i cosh m] ( 2 i N ) i = κ [ θ i+ 1 θ i cosh m] ( 1 i N 1 ) + 1 = κθ1 ( 1 ) = ( 1 cosh m) q cosh m N κθ (3.18) N where G T θ i = Tbi Ta (3.19) U L The useful energy gain to the tubes is given by equations q useful = q i DU θ L i q useful ( T T ) bi fi = (3.20) R

37 37 where the quantity [-DU L θ i ] is the energy collected per unit time and per unit length above the tube. Below is a representation of the finite difference technique. The values of q represent useful energy, given by equations 3.20, transferred to the tube from the upper and lower parts of the absorber plate and γ is an intermediate temperature. Figure 3.9 Representation of the finite difference technique The heat transferred to each node is represented in equations ) ( ) ( ) ( ) ( ) ( 2 ) ( Y q T mc Y q mc Y q q mc Y q mc Y q T mc p p p p p = = + = = = γ γ γ γ γ γ γ γ & & & & & (3.21)

38 38 where γ γ γ γ 2 + γ 2 + γ = T 2 = T 3 = T 5 = T 4 Special care was taken in the algorithm to ensure the boundary conditions at each turn were met. The boundary condition in the above example is T 3 =T 4. This finite difference algorithm was implemented in an EES program, appendix C. EES, Engineering Equation Solver (Klein and Alvarado, 1997), is a computer program that solves sets of equations using matrix techniques. The program was set up in order to enable any number of turns and any number of nodes. The main advantage of this finite difference technique is that no assumptions were made that implied that the technique would only work under certain flow or geometry conditions, such as & c / F U A being greater than unity. m p 1 L c When using a finite difference technique, the major concern is the grid size. In this case, the concern was ensuring that the number of nodes was sufficient to accurately model the problem. Sensitivity of the results to the number of nodes was determined for N=4 and N=10 ; the results are presented in Figure 3.10.

39 N=10 20 nodes 40 nodes N=4 20 nodes 40 nodes 60 nodes FR m/a c [kg/s.m 2 ] Figure 3.10 Sensitivity to the number of nodes in the finite difference technique. It can be seen that the finite difference technique is sensitive to the number of nodes. For the N=4 serpentine collector, 20, 40 and 60 nodes were used. The sensitivity is more marked for the higher flow rates. Little difference was seen between the 40 and 60 node solution. In the case of the N=10 serpentine collector only 20 and 40 nodes were tested. A higher number of nodes was not feasible in terms of computational requirements. Again, the largest discrepancy between the number of nodes was seen at the higher flow rates. The finite difference technique was compared to the solution given by Abdel-Khalik. Figure 3.11 represents the comparison between the methods. The collector was chosen to have a constant area of one square meter, thus varying the number of turns changed the tube spacing.

40 40 Constant values for the fluid heat-transfer-coefficient, h fi, of 1500 W/m 2 K and heat loss coefficient, U L of 5 W/m 2 K were used Finite Difference N=10 mc p /F 1 U L A c = Abdel-Khalik N=10 FR Finite Difference N=2 Abdel-Khalik N= Finite Difference N=1 Abdel-Khalik N= m/a c [kg/s.m 2 ] Figure 3.11 Comparison of the finite difference and Abdel-Khalik model The locus of & F U A equal to unity was also plotted. For values of mc p / 1 L c & mc p / 1 F U L A c greater than unity, the Finite Difference and Abdel-Khalik model compare favorably. At all flow rates, the two methods for one and two turns yield identical results. For N=4 the values for the collector heat removal factor compare reasonably within 4% with the largest discrepancies occurring when & F U A is less than unity. The parameter mc p / 1 L c & F U A is equal to unity at a flow rate per unit area of about 0.06 kg/sm 2 with a mc p / 1 L c

41 serpentine model of N=10. Unfortunately, for the region of interest, at low flow rates and high 41 values of the collector heat removal factor, the parameter & F U A is less than unity and mc p / 1 L c Abdel-Khalik s analysis does not hold for N > 2. At a flow rate of kg/s.m 2 the percentage difference in the values of F R for the finite difference and Abdel-Khalik s analysis is about 15 %. The results of Figure 3.11 do not reveal how the collector heat removal factor is dependent on tube spacing. Figure 3.12 gives an indication of the effects of tube spacing N=1 F R header-riser flat-plate 0.60 N=10 N=4 FR N= Abdel-Khalik Analysis W [m] Figure 3.12 Variation of tube spacing and number of turns

42 42 There is an asymptote for F R at a tube spacing of about 1 cm. The Figure reveals that the minimum value for F R occurs when N=2 and the maximum value occurs when N=1. As the number of turns increases, the values of F R approach the values of F R for N=1, therefore it can be postulated for N= the values of F R equal the values of F R at N=1. This agrees with the results obtained by Zhang and Lavan. The effect of the number of turns for a given tube spacing of 10 cm is shown in Figure F R header-riser flat-plate N=1 0.8 N=10 N=3 N=5 mc p /F 1 U L A c > N=2 FR W=0.1 m m/a c [kg/s.m 2 ] Figure 3.13 Effect of the number of turns on collector performance The results are also presented as the ratio of F R to F R,flat (for various numbers of turns), shown in Figure 3.14.

43 N= N=5 N=10 N=3 N= F R/ F R,flat m/a c [kg/s.m2] Figure 3.14 Comparing the number of turns of the serpentine collector to the one turn collector The difference for F R between the 15 turn serpentine collector and the flat-plate collector is at worst less than five percent for a flow rate of kg/s.m 2. This flow rate is well below the expected operating range. For a flow rate of kg/s.m 2 the difference between the models is less than 3 percent. A serpentine collector may have more than 15 turns. In this case, the analysis for a long straight collector with no turns will hold. Therefore, the model is very close to the model for the flatplate collector, with the exception being that the internal heat transfer coefficient will be different. A collector of N=1 could also be made by using a conventional collector with many turns and creating long cuts between the tubes, effectively decoupling the collector tubes.

44 44 The internal heat transfer coefficient is dependent on the flow rate through the tubes, the diameter of the tubes, the length of the tubes and the flow regime, that is, whether it is laminar or turbulent. For laminar flow (Reynolds numbers less than 2100), the Nusselt number is given by equation 3.21, developed by Heaton et al (Incropera and DeWitt, 1990) for the case of constant heat rate ( Re Pr Di L) ( Re Pr D L) Nu = (3.22) i where Re is the Reynolds numbers, Pr, is the Prandtl number, D i (m) is the tube diameter and L (m) is the tube length. In the turbulent flow regime, Reynolds numbers greater than 2100, the Nusselt number is given by Gnielinski s modification of the Petukhov equation (Incropera and DeWitt, 1990) for Reynolds numbers between 3000 and 5 x10 6, shown in equation f (Re 1000) Pr 8 Nu = (3.23) 1 2 f Pr 1 8 In the above equation, f, represents the friction factor from the Moody chart.

45 3.4 Design Considerations 45 Many design parameters need to be optimized. The fin efficiency gives an indication of the ratio of the heat transfer rate from a fin to the heat transfer rate that would be obtained if the entire fin surface area were to be maintained at the same temperature as the primary surface. The fin efficiency assumes that there is no contact resistance at the fin base. Figure 3.12 gives an example of the effect that the variation of tube spacing had on the collector heat removal factor. The increasing value for F R at decreasing values of tube spacing is related to the fin efficiency as the fin length approaches zero the fin efficiency approaches 100 %. In this region of the curve, there are no losses, but at the same time, the area subject to incident radiation has been greatly reduced. Figure 3.15 shows the fin efficiency curve.

46 design range hfin Figure 3.15 Fin efficiency curve (U L /kd) 1/2 (W-D)/2 A general rule of thumb is that the fin efficiency should be about 90 to 95 %. Higher efficiencies do not tend to be cost effective for this increased efficiency. The above Figure is in terms of the U L design parameter, kδ 1 2 ( W D) 2, where U L (W/m 2 K) is the loss coefficient, W (m) is the tube spacing, D (m) is the tube diameter, k (W/m.K) is the plate conductivity and δ (m) is the plate thickness. The fin efficiency has been represented for the case of one turn. Figure 3.16 represents the effect of tube diameter for a given flow rate of kg/s.m 2. It can be seen that the tube diameter plays little importance in the collector heat removal factor for the header-riser flat-plate collector. However, the tube diameter is very important in serpentine collectors. In order to promote turbulent flow, the tube diameter should be small.

47 serpentine flat-plate FR header-riser flat-plate D [inch] Figure 3.16 Effect of tube diameter on collector performance The fin efficiency was plotted against the tube spacing for plate thicknesses of m and m in Figure The copper tubing chosen has an outer diameter of 1/4 inch and an inner diameter of inches. The plate conductivity is 385 W/m.K.

48 hfin 0.92 design region δ= m δ= m W [m] Figure 3.17 Optimisation of the plate thickness and tube spacing for 1/4 inch diameter tube The serpentine collector needs to be optimised in terms of the plate thickness, tube spacing and tube diameter. As stated earlier, increasing the number of turns will increase the collector heat removal factor. A tube spacing of 10 cm was chosen with a plate thickness of 0.2 mm. Solar collector designs seem to be dictated by the size of the glass cover. In order to decrease costs standard sizes are chosen. Consequently, a 60 x 84 sheet of glass will be used, which is aproximately the size of a patio door, and it is about the maximum size that can be comfortably handled. The serpentine collector model was tested under two configurations: with the tubing parallel to the long side of the collector and parallel to the short side of the collector. The finite difference

49 49 model was used to asses the two configurations. The model was tested for the same surface area of 0.8 m 2. Three turns were used for the configuration with the tubes running parallel to the short side and one turn for the configuration with the tubes parallel to the long side. These were both compared to the model with no turns shown in Figure There was very little difference between the two configurations, however for low flow rates the configuration with three turns outperformed the one turn model N= N=4 FR N= m/a c [kg/s.m 2 ] h fi =1500 W/m 2 K Figure 3.18 Dependence on collector orientation, tube lengths and number of turns For the collector dimensions of 60 x 80, the collector should have 19 tubes in parallel with 18 turns for optimal low-flow performance. The flat-plate model can readily be used for this number of turns.

50 50 The serpentine collector was compared to the conventional header-riser flat-plate, Figure The serpentine collector has better performance due to the higher heat transfer coefficient at collector flow rates greater than approximately kg/s.m 2. The flow through the serpentine collector is 19 times greater than the flow through each riser of the conventional collector serpentine flat-plate 0.80 header-riser flat-plate laminar to turbulent flow transition 0.60 FR m/a c [kg/s.m 2 ] Figure 3.19 Comparison of the heat removal factor for the header-riser and serpentine flat-plate collectors

51 51 The reason why serpentine collectors have been disregarded in the past is because of the belief that the pressure drop would be too large. Figure 3.20 represents the pressure drop across the collectors Pressure Drop header-riser [kpa] serpentine collector header-riser collector Pressure Drop Serpentine [kpa] m/a c [kg/s.m 2 ] Figure 3.20 Comparison of the pressure drop across header-riser and serpentine flatplate collectors The pressure drop for the serpentine collector is much higher, however for a flow rate of kg/s.m 2, the pressure drop of the serpentine collector is approximately 15 kpa. This pressure drop is equivalent to a head of 1.45 m of water. Figure 3.21 represents the pumping power requirements for the serpentine collector.